7.Find the present value.Amount Needed: $42,000Time (Years): 8Rate: 3%Compounded: semiannually$37,283.82$36,960.00$33,097.26$33,155.22

To solve this we are going to use the formula for a future value: [tex]FV=PV(1+ \frac{r}{n} )^{nt}[/tex]
where
[tex]FV[/tex] is the future value 
[tex]PV[/tex] is the present value 
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the time in years

Since the amount needed is $42,000, [tex]FV=42000[/tex]. We also know for our problem that [tex]t=8[/tex] and [tex]r= \frac{3}{100} =0.03[/tex]. Since the interest is compounded semiannually, it is compounded two times per year; therefore, [tex]n=2[/tex]. Lets replace those values in our formula and solve for [tex]PV[/tex]:
[tex]FV=PV(1+ \frac{r}{n} )^{nt}[/tex]
[tex]42000=PV(1+ \frac{0.03}{2})^{(2)(8)} [/tex]
[tex]PV= \frac{42000}{(1+ \frac{0.03}{2})^{(2)(8)}} [/tex]
[tex]PV=33097.30[/tex]

We can conclude that the present value needed to make $42000 after 8 years according to your given choices is $33,097.26